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CONTENTS
Volume 8, Number 5, November 1999
 

Abstract
A simple numerical scheme suitable for tracing the fracture propagation path for structures idealized by means of Hillerborg\'s classical cohesive crack model is presented. A direct collocation, multidomain boundary element method is adopted for the required space discretization. The algorithm proposed is necessarily iterative in nature since the crack itinerary is a priori unknown. The fracture process is assumed to be governed by a path-dependent generally nonlinear softening law. The potentialities of the method are illustrated through two examples.

Key Words
cohesive crack, crack propagation, quasibrittle fracture, softening.

Address
Tin-Loi F, Univ New S Wales, Sch Civil & Environm Engn, Sydney, NSW 2052, Australia
Univ New S Wales, Sch Civil & Environm Engn, Sydney, NSW 2052, Australia

Abstract
Safety monitoring systems of structures generally resort to detecting possible changes of dynamic system parameters. Sensitivity analysis of these dynamic system parameters may implement these techniques. Conventional structural eigenvalue problems are discussed in the scope of those systems with deterministic parameters. Large and flexible structures, such as suspension bridges, actually possess stochastic material properties and these random properties unavoidably affect the dynamic system parameters. The sensitivity matrix of structural modal parameters to basic design variables has been established in this paper. Moreover, second order statistics of natural frequencies due to the randomness of material properties have been discussed. It is concluded from numerical analysis of a modem suspension bridge that although the second order statistics of frequencies are small relatively to the change of basic design variables, such as density of mass and modulus of elasticity, the sensitivities of modal parameters to these variables at different locations change in magnitude.

Key Words
stochastic finite element method, suspension bridge, sensitivity, free vibration

Address
Liu CH, Tsing Hua Univ, Dept Civil Engn, Beijing 100084, Peoples R China
Tsing Hua Univ, Dept Civil Engn, Beijing 100084, Peoples R China
Florida Int Univ, Dept Civil & Environm Engn, Miami, FL 33199 USA

Abstract
A structural optimization process is presented for arches with varying cross-section. The optimality criteria method is used to develop a recursive relationship for the design variables considering displacement, stresses and minimum depth constraints. The depth at the crown and at the support are taken as design variables first. Then the approach is extended by taking the depth values of each joint as design variable. The curved beam element of constant cross section is used to model the parabolic and circular arches with varying cross section. A number of design examples are presented to demonstrate the application of the method.

Key Words
optimization of arches, arch bridges, curved beams, circular arch element, parabolic arch element

Address
Uzman U, Karadeniz Tech Univ, Dept Civil Engn, TR-61080 Trabzon, Turkey
Karadeniz Tech Univ, Dept Civil Engn, TR-61080 Trabzon, Turkey
Univ Bahrain, Dept Civil Engn, Isa Town, Bahrain

Abstract
The uncertainties associated with structural parameters and dynamic loading are identified and discussed. Structural parametric uncertainties are treated as random variables and dynamic wind load is simulated as a random process. Dynamic wind-induced responses of structures with parametric uncertainties are investigated by using stochastic finite element method. The formulas for structural dynamic reliability analysis considering the randomness of structural resistance and loading are proposed. Two numerical examples of high-rise structures are presented to illustrate the proposed methodology. The calculated results demonstrate that the variation in structural parameters indeed influences the dynamic response and the first passage probability evaluation of structures.

Key Words
dynamic response, finite element method, uncertainty, dynamic reliability

Address
Li QS, City Univ Hong Kong, Dept Bldg & Construct, Tat Chee Ave, Kowloon, Hong Kong
City Univ Hong Kong, Dept Bldg & Construct, Kowloon, Hong Kong

Abstract
The initiation of toppling is explored for a uniform stack of blocks that rotates slowly about its mid-base. As the stack passes through its vertical position (theta=0), it is in free-fall rotation, and a critical inclination angle theta(c) is reached at which the toppling stack fails\" or begins to crack or separate. For tall stacks (high aspect ratios), two modes of failure are hypothesized, for which the dynamic failure analyses are shown to correlate with experimental results. These block failure modes are similar to those observed for tall, toppling masonry structures with weak binding material between their brick or stone blocks.

Key Words
block dynamics, block stacks, block toppling, chimney failure, masonry structures, masonry towers, structural dynamics, structural failure, tower failure

Address
Wilson JF, Duke Univ, Dept Civil & Environm Engn, Durham, NC 27708 USA
Duke Univ, Dept Civil & Environm Engn, Durham, NC 27708 USA

Abstract
Based on the concept of the parameter-mixed synthesis, this paper presents a mixed formulation of the substructure synthesis method in terms of the physics-impedance-mo dal parameter. An example is given to show the validity of this method.

Key Words
mixed synthesis, dynamic substructure

Address
Wang JJ, Beijing Univ Aeronaut & Astronaut, Dept Jet Prop, Beijing 100083, Peoples R China
Beijing Univ Aeronaut & Astronaut, Dept Jet Prop, Beijing 100083, Peoples R China

Abstract
A concept of hierarchical modeling, the newest modeling technology, has been introduced in early 1990\'s. This new technology has a great potential to advance the capabilities of current computational mechanics. A first step to implement this concept is to construct hierarchical models, a family of mathematical models sequentially connected by a key parameter of the problem under consideration and have different levels in modeling accuracy, and to investigate characteristics in their numerical simulation aspects. Among representative model problems to explore this concept are elastic structures such as beam-, arch-, plate- and shell-like structures because the mechanical behavior through the thickness can be approximated with sequential accuracy by varying the order of thickness polynomials in the displacement or stress fields. But, in the numerical, analysis of hierarchical models, two kinds of errors prevail, the modeling error and the numerical approximation error. To ensure numerical simulation quality, an accurate estimation of these two errors is definitely essential. Here, a local a posteriori error estimator for elastic structures with thin domain such as plate- and shell-like structures is derived using the element residuals and the flux balancing technique. This method guarantees upper bounds for the global error, and also provides accurate local error indicators for two types of errors, in the energy norm. Compared to the classical error estimators using the flux averaging technique, this shows considerably reliable and accurate effectivity indices. To illustrate the theoretical results and to verify the validity of the proposed error estimator, representative numerical examples are provided.

Key Words
hierarchical model, elastic body, a posteriori error estimator, flux balancing, effectivity index.

Address
Cho JR, Pusan Natl Univ, Sch Mech Engn, Pusan 609735, South Korea
Pusan Natl Univ, Sch Mech Engn, Pusan 609735, South Korea


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